1. The diophantine equation $x^4+y^4=z^4+w^4$
- Author
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Choudhry, Ajai and Zargar, Arman Shamsi
- Subjects
Mathematics - General Mathematics ,11D25 - Abstract
Since 1772, when Euler first described two methods of obtaining two pairs of biquadrates with equal sums, several methods of solving the diophantine equation $x^4+y^4=z^4+w^4$ have been published. All these methods yield parametric solutions in terms of homogeneous bivariate polynomials of odd degrees. In this paper we describe a method that yields three parametric solutions of the aforesaid diophantine equation in terms of homogeneous bivariate polynomials of even degrees, namely degrees~$74$, $88$ and $132$ respectively., Comment: 8 pages
- Published
- 2024